In the year 2019, R has invested for six months only while Q and P invested for the whole year. Find the total profit earned during the year 2019.

Steps to Solve

1. Identify Profits and Shares in 2019 R's investment duration is 6 months, while P and Q invested for the entire year. We know Q's profit in 2019 is not given but needs to be derived.

2. Understanding the Total Profit in 2019 From the table, the total profit for 2019 is given as ( 19200 ). This total is the sum of profits earned by P, R, and Q: $$ P + R + Q = 19200 $$

3. Find Profit Earned by P From the table, it is clear that P's profit in 2019 is given as ( 6400 ).

4. Substitute Known Values into the Equation We substitute P's profit into the total profit equation: $$ 6400 + R + Q = 19200 $$

5. Rearranging the Equation Now, we can isolate R and Q: $$ R + Q = 19200 - 6400 $$ $$ R + Q = 12800 $$

6. Determine R's Profit Now we know that R, who invested for 6 months, will earn a proportion of the total profit. Since R invested for half of the year, R's profit can be expressed as: $$ R = \frac{6}{12} \times 12800 $$ $$ R = 0.5 \times 12800 $$

7. Calculate R's Profit Calculating this gives: $$ R = 6400 $$